Problem 21 · 2020 Math Kangaroo
Medium
Logic & Word Problems
careful-counting
In a classroom there are two chairs at each table. Each boy in the class sits at a table with a girl, but there are four girls who do not sit at a table with a boy. There are 14 little tables in the classroom. How many girls are in that class?
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Answer: E — 16
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Hint 1 of 2
Most tables seat one boy and one girl; a few seat two girls.
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Hint 2 of 2
Count the all-girl tables, then add the girls sharing with boys.
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Approach: split tables into boy-girl and girl-girl
- Four girls sit without a boy, two to a table, so 2 tables are all-girl.
- That leaves 14 minus 2 = 12 tables, each with one boy and one girl.
- Total girls = 12 (one per mixed table) plus 4 = 16.
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